CN109656019B - Design method of dielectric super-oscillation ring band piece - Google Patents

Design method of dielectric super-oscillation ring band piece Download PDF

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CN109656019B
CN109656019B CN201910005120.3A CN201910005120A CN109656019B CN 109656019 B CN109656019 B CN 109656019B CN 201910005120 A CN201910005120 A CN 201910005120A CN 109656019 B CN109656019 B CN 109656019B
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刘涛
杨树明
刘康
刘强
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Xian Jiaotong University
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Abstract

The invention discloses a design method of a dielectric super-oscillation ring band sheet, and belongs to the technical field of micro-nano optics and nano photonics. The method is based on a dielectric concentric ring band structure with variable width and depth, and under the condition of vertical illumination of laser beams, a diffraction light field at any distance position behind a super-oscillation ring band piece is calculated by using a vector angular spectrum theory and a fast Hankel transformation algorithm; setting the diameter, the number of ring belts, the maximum phase etching depth, the minimum ring belt width and the focal length of the dielectric super-oscillation ring belt sheet; establishing an optimization model and an optimization objective function of a single focus or light needle focusing problem; and (3) optimizing and solving the radial width and the phase depth of each annular band by adopting and configuring a genetic algorithm to obtain the dielectric medium super-oscillation annular band structure meeting the design target. Compared with the amplitude type super-oscillation ring belt sheet based on the metal film, the planar phase type super-oscillation ring belt sheet with higher optical efficiency, larger view field, easier processing and better practicability is designed and generated.

Description

Design method of dielectric super-oscillation ring band piece
Technical Field
The invention belongs to the technical field of micro-nano optics and nano photonics, and particularly relates to a design method of a dielectric super-oscillation ring band sheet.
Background
The super-oscillation (Superoscillation) is firstly described in a complete theory mathematically, and refers to a special phenomenon that the local oscillation frequency of a frequency domain band-limited function or a signal is faster than the cut-off frequency of the whole function, the super-resolution focusing can be realized by using the Optical super-oscillation (Optical Superoscillation), and the method is widely concerned in the aspect of realizing Optical sub-wavelength focusing and super-resolution imaging in the near decade, and is essentially in the far-field Optical category, independent of the contribution of near-field evanescent waves, and the super-resolution focusing is generated by using the coherent superposition of far-field transmission fields.
In 2009, a special continuous amplitude transmittance function is theoretically constructed by the university of southampton in england, however, a mask plate described by the continuous complex amplitude transmittance function requires a very harsh coating process and photoetching technology; in 2012, the university of south ampatondon proposed a significant improvement, and proposed a Super-oscillating Lens (SOL) (see documents e.t.f. rogers, j.lindberg, t.roy, s.savo, j.e. chad, m.r. dennis, n.i. zheluedv.asuper-oscillatorylns optical microscopic for subwavelength imaging. naturemetals, 2012,11(5), 432-. The basic hypothesis and design thought of English researchers are continued, and the national Harbin industry university, the Sigan traffic university, the northwest industry university, the institute of photoelectric technology of Chinese academy of sciences, the Nanjing university and the like carry out highly effective research on the aspects of theoretical design, preparation, application and the like of the metal film super-oscillation ring band sheet. In particular, in the research of phase type super-oscillation ring strips, theory of Liutao, et al, Harbin university of industry designed binary phase type super-oscillation ring strips (see documents T. Liu, J. Liu, H. Zhang, J.Tan. effective optimization of super-oscillation lens and transfer function analysis in semiconductor communication, 2014,319:31-35), Cheng et al, Chongqing university, conducted in-depth research on one-dimensional linear super-oscillation structures and two-dimensional phase type super-oscillation ring strips (see documents Z.Chen, Y.Zhang, M.Xiao.Deng.of oscillator for a polar oscillation, journal of super-oscillation ring strips, 2015: 32, and binary phase amplitude ring strips designed by Liutao, et al, Beijing university of industry, Bian, et al, super-oscillation ring strips, III, Bin. Zhang, M.Xiao.D.A.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.
The above research designs all assume equal-width annuli and fixed phase etching depths, which are the main problems faced by the current phase type super-oscillation annulus design, and therefore it is urgent to provide a general design method for a phase type dielectric super-oscillation annulus with free widths and free depths of each sub-annulus.
The focusing device designed by the prior art (national invention patent: Chenggang, hot spring, Wuzhixiang, Yuanping, a multi-value phase-binary amplitude super-diffraction hollow halo focusing device, patent application No. 201610599066.6, application date 2016, 7, 27, Chenggang, Wuzhixiang, hot spring, Zhangyi, Beam height, a far-field super-diffraction three-dimensional hollow focal spot plane focusing device, patent application No. 201810220342.2, application date 2018.03.16) takes an equal-width annular zone as a basic assumption, belongs to the technical method category of the traditional super-oscillation annular zone, adopts a binary or multi-value phase which is multi-step, and therefore, the method has substantial significant difference from the design method directly derived from the unequal-width annular zone assumption, and simultaneously constrains the phase depth to an effective range.
Disclosure of Invention
The invention aims to provide a design method of a dielectric medium super-oscillation ring band plate with larger degree of freedom, higher focusing efficiency and better performance, and a plane dielectric medium super-oscillation ring band plate structure which can be practically used is designed by parameter setting, establishment of an optimized objective function and solution of an optimized algorithm under the condition of vertical illumination of a typical polarization state laser beam.
The invention is realized by adopting the following technical scheme:
a design method of a dielectric super-oscillation ring band piece is characterized in that based on the variable radial width and variable phase etching depth of a ring band of the dielectric super-oscillation ring band piece, under the condition of vertical illumination of a laser beam, a diffraction light field in a plane at any distance from a vertical axis behind the dielectric super-oscillation ring band piece is calculated by using a vector angle spectrum theory and a fast Hankel transformation algorithm; setting the diameter, the ring belt number, the focal length, the minimum ring belt width and the maximum phase etching depth of the dielectric super-oscillation ring belt sheet; blocking incident laser beams by a metal-plated film in the area outside the diameter of the dielectric super-oscillation ring belt sheet; establishing an optimized objective function of a single focus or light needle focusing problem; and (3) optimizing and solving the etching width and the etching depth of the girdle by adopting a genetic algorithm to obtain the dielectric super-oscillation girdle plate structure meeting the design target.
The invention is further improved in that the dielectric super-oscillation ring band plate is a binary phase type super-oscillation ring band plate, and phase modulation of incident light waves is realized by etching each ring band on the surface of the dielectric material to the optimally set depth.
A further improvement of the invention is that the method comprises in particular the steps of:
step one, giving the required diffraction light field intensity distribution characteristics of the dielectric super-oscillation annular zone plate, and respectively constraining the diffraction intensity field in the transverse direction and the axial direction according to the required diffraction light field intensity distribution to establish an optimized objective function and constraint conditions;
setting the diameter, the number of annuli, the maximum phase etching depth, the minimum annulus width and the focal length of the dielectric super-oscillation annuli, the wavelength and the polarization state of the illumination laser beam, and the dielectric material and the working medium of the dielectric super-oscillation annuli;
thirdly, under the parameter setting of the second step, calculating the light field intensity distribution in the vertical axis plane at any distance behind the super-oscillation ring band sheet through a vector angle spectrum theory and a fast Hankel transform algorithm;
and step four, solving the dielectric super-oscillation annular band piece structure meeting the optimization target established in the step one by adopting a genetic algorithm on the basis of the variable annular band radial width and the variable phase etching depth of the dielectric super-oscillation annular band piece.
The invention is further improved in that the width of each ring belt contained in the designed super-oscillation ring belt sheet is variable, the phase etching depth of each ring belt of a single super-oscillation ring belt sheet is consistent, the etching depth is variable for different super-oscillation ring belt sheets, and the width of each ring belt and the etching depth are optimized and solved through a genetic algorithm.
In a further improvement of the invention, in the first step, the diffraction light field intensity distribution characteristics of the dielectric ultra-oscillating annular strip include transverse full width half maximum, axial full width half maximum of the focusing spot, or transverse full width half maximum, axial focal depth and axial light intensity uniformity of the focusing light needle.
The further improvement of the invention is that in the step one, the specific method for establishing the optimization objective function is as follows: according to the required full width at half maximum and focal depth of the focusing light spot or the light needle, respectively finding out the half-height point of the transverse and axial focusing light spot or the light needle, and solving the ratio F of the light intensity at the position of the half-height point to the light intensity at the central position of the focusing light spot or the light needlexyAnd FzThe ratio is the established transverse and axial optimization objective function respectively; the optimization objective function in two directions passes through the set weighting coefficient w1And w2Are synthesized into a total optimization objective function F ═ w1/Fxy+w2/FzAnd converting the multi-objective optimization problem into a single-objective optimization problem.
The invention is further improved in that the stepsThe specific setting requirements of the super-oscillation ring band piece in the second step are as follows: the diameter D is more than or equal to 5 lambda0，λ0The wavelength of the illumination laser in vacuum is in the range from X-ray to far infrared band, and the focal length satisfies that f is more than or equal to lambda0The number N of the ring belts is more than or equal to 2, and the maximum phase etching depth delta phimaxLess than or equal to pi/2 and the minimum annulus width delta rminMore than or equal to 200 nm; the polarization state of the illumination laser beam is linear polarization, circular polarization, radial polarization or angular polarization, and the refractive index n of the dielectric materialdGreater than 1, the working medium is air, oil or water, the refractive index n of the working mediumw≥1。
The further improvement of the invention is that the vector angular spectrum theory stated in the third step means that firstly the angular spectrum of the light field emitted from the rear surface of the microstructure is obtained through one Fourier transform, and then each polarization component of the plane light field of the observation position is obtained through one inverse Fourier transform, so that the intensity distribution of the light field in the vertical axis plane of any distance behind the super-oscillation ring band plate is obtained through calculation when the laser beam vertically illuminates the super-oscillation ring band plate; the fast Hankel transformation algorithm is a fast and high-precision calculation method for calculating cross-correlation by utilizing Fourier transformation by performing variable replacement by utilizing a nonlinear exponential function in a standard Hankel transformation integral expression and expressing standard unilateral Hankel transformation as bilateral cross-correlation integral.
The invention is further improved in that the designed real etching depth of the dielectric medium corresponding to the phase etching depth of the dielectric medium super-oscillation ring band plate meets the requirement of the real etching depth of the dielectric medium
Figure BDA0001935134870000041
φiFor phase etch depth, ndAnd nwDielectric and working medium refractive indices, respectively; phase etching depth phi of dielectric super-oscillation ring band plateiThe zone of (a) corresponds to a phase modulation function of ti(r)＝exp(-jφi),ri-1≤r＜ri。
The invention is further improved in that the optimization design process of the genetic algorithm in the step four is as follows:
401) and (3) carrying out an encoding operation: coding the width and the etching depth of each ring belt respectivelyWherein the width of the N zones passes through the interval [0, R ] between 0 and the radius R of the super-oscillating zone plate]N-1 dividing points generated internally at random are obtained, and the positions of the dividing points are coded by decimal numbers; phase etching depth phi of each ring belt of single ring belt sheetiThe same, coded by one decimal number, takes on the interval phii∈[0,π/2](ii) a The zone etching zone bit of the dielectric super-oscillation zone piece is coded by a one-bit binary number, the zone bit is 1 to indicate that the zone is etched, and the zone bit is 0 to indicate that the zone is not etched;
402) random generation of psThe initial individuals form an initial population, the loop widths of the initial individuals are checked, individuals which do not meet the requirement of the minimum loop width are removed, new individuals are regenerated until all the individuals in the initial population meet the requirement; then, an optimized objective function value F of each individual is calculated according to the optimized objective function established in the step onei，i＝1,2,…,ps；
403) In order to improve the optimization design efficiency, constraint conditions in the optimization model are written into a set optimization objective function and are incorporated into a total objective function, and the ratio of the maximum light intensity in the dark field region required to be taken out of the dark field region to the central light intensity of the main lobe is taken as an objective function FdAnd are combined into a total objective function F with a set weighting coefficient to obtain F ═ w1/Fxy+w2/Fz+w3/Fd；
404) And (3) carrying out selective copying operation: the selection strategy adopts a method of combining an elite individual retention strategy and roulette, and directly copies the individual with the highest fitness in the contemporary population into the next generation without crossing and mutation operations; the other individuals are selected according to a roulette method by first determining respective selection probabilities according to respective fitness values of all individuals
Figure BDA0001935134870000051
Then in [0,1 ]]Randomly generating a random number r in the interval if
Figure BDA0001935134870000052
Then select individual i to copy to the next generation, where P0＝0；
405) Performing a cross operation: according to the cross probability PcRandomly generating a random number for every two individuals, if the random number is less than or equal to PcIf not, the two individuals are subjected to the cross operation; the crossing operation adopts a uniform crossing method, firstly, a binary crossing template with the same length as the parent individual is randomly generated, wherein 0 represents that the corresponding position is not exchanged, and 1 represents that the corresponding position is exchanged; after each pair of individuals are subjected to the cross operation, judging whether the generated new individuals meet the requirement of the minimum bandwidth, and if not, carrying out the cross operation again;
406) according to the mutation probability PmRandomly generating a random number for each individual, if the random number is less than or equal to PmIf not, the individual does not carry out mutation operation; the variation operation adopts single point variation, if the variation point is a dividing point for determining the width of the ring band, then [0, R ] is taken]Random numbers uniformly distributed in the interval replace selected individual genes; if the variation is the annular phase etching depth of the dielectric super-oscillation annular plate, then [0, pi/2 ] is taken]Replacing the ring phase etching depth of the dielectric super-oscillation ring band piece by random numbers uniformly distributed in the interval; if the variation is the zone bit for determining whether each zone of the dielectric super-oscillation zone piece is etched, negating the zone bit, namely changing the zone etching 1 into the zone non-etching 0 or changing the zone non-etching 0 into the zone etching 1; judging whether the generated new individual meets the requirement of the minimum bandwidth after each individual mutation operation is finished, and if not, carrying out the mutation operation again;
407) generating a new offspring population after the selection, the crossing and the variation are finished, calculating objective function values of all individuals of the offspring population, replacing the original parent population with the new offspring population, returning to the step 404 of the genetic algorithm), carrying out a new iteration, and repeating the steps until the set iteration number N is reachedg；
408) Number of iterations completed NgLater, the hereditary excelsThe chemical process is finished, and the final optimization result is NthgThe individuals with the highest fitness in the generation group are required to be the dielectric super-oscillation annular belt structure which is close to or meets the set diffraction light field intensity distribution.
The invention has the following beneficial technical effects:
the invention provides a method for designing a phase type super-oscillation ring band plate with higher light-emitting efficiency, larger degree of freedom and certain field of view, which is based on a dielectric concentric ring band structure with variable width and variable depth, and under the condition of typical polarized light vertical illumination, a vector angular spectrum theory and a fast Hankel transformation algorithm are used for calculating a diffraction light field at any distance position behind the super-oscillation ring band plate; setting the diameter, the number of ring belts, the maximum phase etching depth, the minimum ring belt width and the focal length of the dielectric super-oscillation ring belt sheet; establishing an optimization model and an optimization objective function of a single focus or light needle focusing problem; and (3) optimizing and solving the radial width and the phase depth of each annular band by adopting and configuring a genetic algorithm to obtain the dielectric medium super-oscillation annular band structure meeting the design target. Compared with the amplitude type super-oscillation ring belt sheet based on the metal film, the planar super-oscillation ring belt sheet with higher optical efficiency, larger view field and easier processing is designed and generated. The method is suitable for various typical polarized laser beam illumination situations, the designed dielectric medium super-oscillation ring band sheet can be practically applied to the fields of super-resolution focusing, far-field nano-microscopic imaging, nano-lithography, laser micromachining, optical control and the like, and conventional refraction lenses and lens groups can be replaced on certain occasions.
Drawings
Fig. 1 is a schematic cross-sectional view of a dielectric super-oscillation ring segment according to the present invention, in which fig. 1(a) is a front view, fig. 1(b) is a top view, reference numeral 1 is a metal film, reference numeral 2 is an etched ring segment of a prescribed depth, and reference numeral 3 is an unetched ring segment.
FIG. 2 is a graph of the etch depth of the dielectric material of the dielectric super-oscillating ring plate in an embodiment of the present invention (the dotted line indicates that the upper limit of the etch depth of the corresponding confined phase is π/2).
Fig. 3 is a graph comparing the result of the vector Angular Spectrum theory (VAS) design of the y-directional optical field intensity distribution of the dielectric super-oscillating ring band plate focal plane with the result of the strict electromagnetic simulation calculation (FDTD) in the embodiment of the present invention.
Fig. 4 is a graph comparing the theoretical design result of the vector angular spectrum of the z-direction optical field intensity distribution on the optical axis of the dielectric super-oscillation ring band with the calculation result of the FDTD strict electromagnetic simulation in the embodiment of the present invention.
FIG. 5 is a FDTD rigorous electromagnetic simulation calculated intensity profile of the superoscillatory ring band slab focal plane in an embodiment of the present invention.
FIG. 6 is a graph of FDTD rigorous electromagnetic simulation computed intensity distribution of the axial X-Z plane of a dielectric superoscillatory ring plate in an embodiment of the present invention.
FIG. 7 is a FDTD rigorous electromagnetic simulation computed intensity profile of the axial Y-Z plane of a dielectric superoscillatory ring plate in an embodiment of the present invention.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the drawings and examples.
In this embodiment, the optical field focusing by the dielectric super-oscillating ring strip is taken as an example for explanation. Modulating an incident diffraction light field by using a dielectric super-oscillation annular band piece as shown in figure 1, realizing focusing of the light field in a specific area away from the rear surface of the annular band piece, and performing light field diffraction propagation analysis by using a vector angular spectrum theory; in fig. 1, the reference numeral 1 is a 100nm metal aluminum film, the reference numeral 2 is a dielectric ring zone with the etching depth of 308.8nm, and the reference numeral 3 is a non-etching ring zone; on the basis that the widths of the super-oscillation ring belt pieces are unequal and the etching depth among the ring belt pieces is variable, a genetic algorithm is utilized to solve the dielectric super-oscillation ring belt piece structure meeting the optimization target.
(1) Vector angular spectrum theoretical light field calculation
Assuming that linearly polarized light vibrating along the X-axis direction is positively transmitted along the Z-axis, the surface of the super-oscillation zone plate is vertically illuminated, after diffraction by the micro-structure zone, the light is diffracted at the Z-axis according to the vector angular spectrum theory>0 at any point in the vertical axis plane
Figure BDA0001935134870000086
At a right angle component of the electric field E of
Figure BDA0001935134870000081
In the formula, Ex(r, z) denotes the x-directional component, Ey(r, z) represents a y-directional component,
Figure BDA0001935134870000082
denotes the component in the z direction, q (l) ═ 1/lambda2-l2)1/2And l represents a radial spatial frequency component; r represents the distance of any point P in the vertical axis plane with respect to the intersection of the plane and the optical axis,
Figure BDA0001935134870000083
the positive included angle of the point P relative to the X axis is shown, and the axial position of the vertical axis plane where the point P is located is shown in z; j. the design is a square0And J1Respectively, a first class zero order and first order Bessel function, j being an imaginary unit; space angle spectrum A0(l) Is shown as
Figure BDA0001935134870000084
Wherein t (r) represents the phase modulation function corresponding to any circularly symmetric ring band piece, and the phase modulation function corresponding to each ring band is specifically represented as
ti(r)＝exp(-jφi),ri-1≤r＜ri(3)
Wherein i is 1,2, N is the number of zones included in the dielectric super-oscillation zone piece, r is0＝0；φiIs the phase etching depth and the actual etching depth hiThe relationship between is
Figure BDA0001935134870000085
In the formula, ndAnd nwDielectric and working medium refractive indices, respectively; h isi0 corresponds to t i1. In the formula (2), g (r) representsThe optical field amplitude of the bright beam in the microstructure zone slab plane, assumed here as uniform plane wave illumination, corresponds to g (r) ═ 1. The intensity distribution of the optical field after the dielectric super-oscillation ring band sheet can be obtained by the formula (1)
Figure BDA0001935134870000091
When the illumination laser beam is left-handed circularly polarized light, the components of the electric field E are:
Figure BDA0001935134870000092
in the formula, A0(l) Is given by formula (2).
Similarly, the intensity distribution of the optical field after the super-oscillation ring-band is I (r, z) ═ 2| Ex(r,z)|2+|Ez(r,z)|2。
According to the formulas (1), (2) and (5), the light field distribution in any vertical axis plane can be calculated respectively when linearly polarized light and circularly polarized light illuminate the super-oscillation annular band sheet, and the light field distribution under the condition of radial and angular polarized light illumination can be calculated in the same way.
(2) Fast hankel transformation algorithm
In the calculation process of the formula (1), the formula (2) and the formula (5), a large amount of zero-order and first-order Hankel transformation is required to be executed, so the calculation efficiency and precision of the Hankel transformation are the key of a design method, in order to accelerate the operation, a Fast Hankel transformation algorithm is realized through programming (see the documents A.E.Siegman.Quasi Fast Hankel transform. optics Letters,1977,1:13-15), the algorithm has the remarkable advantages of high calculation speed, high precision, extremely low computer storage requirement and the like, and the basic principle is that in a standard Hankel transformation integral expression, a nonlinear exponential function variable is used for replacing, the standard unilateral Hankel transformation is expressed as bilateral cross-correlation integral, and after the transformation, Fourier transformation can be used for calculating the cross-correlation.
(3) Detailed description of the preferred embodiments
The diffraction light field intensity distribution characteristics of the dielectric super-oscillation ring band sheet are set as follows: transverse half height of focused light spotFull width FWHMxy＝0.4λ0Axial depth of focus DOF ═ λ0，λ0Is the wavelength of the illuminating laser.
Using wavelength λ0Vertical illumination with 633nm X-direction linearly polarized laser beam, air as working medium (refractive index n)w1) and the dielectric material is quartz glass (refractive index n)d1.457) designing the diameter D of the super-oscillation ring band piece to be 14 mu m, the focal length f to be 3 mu m, the ring band number N to be 10 and the minimum ring band width DeltarminMaximum phase etching depth phi of 200nmmax＝π/2。
The established optimization model is as follows:
Figure BDA0001935134870000101
among them, FWHMxyIs the transverse full width at half maximum of the diffraction focusing spot, f is the focal length, phiiIs the phase depth of each zone, wherein I represents the number of each zone of the super-oscillation zone plate, and the values I are 1,2, …, N, I (FWHM) from inside to outside in sequencexy/2,f,ri,φi) Denotes the light field intensity at the full width half maximum of the transversely focused spot, I (0, f, r)i,φi) The light field intensity of the central position of the transverse focusing light spot; i (0, f)-,ri,φi) And I (0, f)+,ri,φi) The two full-width half-maximum points f on the left and the right of the main lobe of the focusing light spot on the Z-direction axis respectively-And f+The intensity of the light field of (a).
In order to enable the designed super-oscillation ring band plate to be used for high-resolution focusing imaging, a central main lobe and surrounding high-order side lobes need to be separated by a dark field area which is wide enough, so that the following constraints are made on a diffraction light field:
Figure BDA0001935134870000102
the value range of the dark field region of the transverse focusing light field in the formula (7) is a region from one half-maximum width to three times of the half-maximum width away from the center of the main lobe, so that the main lobe light field is fully separated from the surrounding high-order side lobe light field; because the design requirement is axial single focus focusing, the light field intensity of the rest areas except for one focus depth DOF distance from the center position of the focus on two sides of the axial focusing light spot is restrained.
Under the optimization objective function and the constraint conditions, the total optimization objective function of the genetic algorithm is established as follows:
Fitness＝w1/Fxy+w2/Fz+w3/Fs,xy+w4/Fs,z(8)
wherein the content of the first and second substances,
Figure BDA0001935134870000111
and
Figure BDA0001935134870000112
is an optimization objective function converted from the constraint condition; taking w as weight coefficient of each optimized objective function1＝w2＝0.85，w3＝w40.15; the original solution of the super-oscillation ring band piece optimization structure problem for realizing the setting of the light field intensity distribution is converted into the solution of the maximum value problem of the optimization objective function Fitness (or Fitness function).
The individual chromosome coding strategy of the genetic algorithm is: the total number of N +1 chromosome codes of each individual, the first N-1 chromosome decimal codes, which represent the positions of the division points determining the width of each ring zone, and the interval [0, R ] from 0 to the radius R of the super-oscillation ring zone]Internally generating randomly to obtain; phase etching depth phi of each ring belt of single ring belt sheetiThe same is coded by the decimal number of the Nth chromosome, and the value interval phi is takeni∈[0,π/2](ii) a The zone etching flag bit of the dielectric super-oscillation zone piece is coded by the last binary number of the chromosome, the flag bit is 1 to indicate that the central zone of the zone piece is etched, and the flag bit is 0 to indicate that the central zone of the zone piece is not etched; the set genetic algorithm optimization parameters are as follows: number of individuals p of initial populations80, total number of iterations of genetic manipulation Ng60; genetic selection and replication adopt a method of combining an elite individual retention strategy with roulette; the cross operation adopts a uniform cross method and a cross probability Pc＝0.8；The mutation operation is carried out by single-point gene mutation with a mutation probability Pm＝0.01。
The genetic algorithm is realized according to the parameter programming, the ring structure and the etching depth of the dielectric medium super-oscillation ring band piece obtained by optimization solution are shown in table 1, and the geometric structure parameters and the focusing characteristics of the dielectric medium super-oscillation ring band piece are shown in table 2. Wherein N isiIs the number of the girdle, the number is 1 to 10 from inside to outside, delta riAnd hiThe width and etching depth of each ring belt, NtThe number of the light-transmitting ring belts; h isetchRepresenting the etching depth; the transverse dimension of the focused light spot is represented by a full width half maximum value, the longitudinal dimension of the focused light spot is represented by a focal depth, and specific numerical values are all represented by multiples of incident laser wavelength.
TABLE 1 Ring band width and etch depth of dielectric super-oscillating ring band plate
Figure BDA0001935134870000113
TABLE 2 surface zone structural parameters and focusing characteristics of dielectric superoscillatory zone plates
Figure BDA0001935134870000121
As can be seen from tables 1 and 2, the minimum bandwidth of the design result is 202nm, which is greater than the given minimum bandwidth, and meets the requirements; the designed dielectric medium super-oscillation ring belt sheet only comprises 5 light-transmitting ring belts, the numerical aperture NA reaches 0.92, and the full width at half maximum in the y direction of a focal plane focusing light spot is 0.547 lambda0The axial focal depth also reaches 1.453 lambda0The full widths at half maximum in the transverse x-axis direction and the transverse y-axis direction are not equal, and the focusing light spots are dumbbell-shaped, which is the basic focusing characteristic of the incident situation of the linearly polarized light with large numerical aperture.
In the focusing dielectric super-oscillation ring belt piece provided in the embodiment, the ring belt etching depth curve of the design result is shown in fig. 2; the vector angle spectrum theory (VAS) calculation result of the dielectric super-oscillation ring band piece is basically consistent with the FDTD strict electromagnetic simulation calculation result, such asFig. 3 and 4 show that the effectiveness of the design method of the dielectric super-oscillation ring band piece is verified. FIGS. 5, 6 and 7 are FDTD rigorous electromagnetic simulation calculated intensity profiles of the X-Y plane, X-Z plane and Y-Z plane of the superoscillatory ring band sheet, respectively. Wherein the focal plane is located at half of the etching depth (i.e. h) of the dielectric super-oscillation ring bandetchThe vertical axis plane of the position of/2) is taken as a reference plane.
The parameters of the three-dimensional FDTD simulation model related in the embodiment are as follows: adopting a full-field scattered field (TFSF) light source, wherein the wavelength is 633nm, and the boundary condition is PML; the dielectric super-oscillation ring belt sheet is made of quartz glass and has a refractive index of 1.457; the working environment is air, and the refractive index is 1; FDTD simulation region is x, y: [ -8,8], z: [ -2,8] (units are μm); taking a vertical axis plane at a position of half of the etching depth of the annular belt as a reference plane (z is 0); the size of the divided grids is 15nm multiplied by 15 nm; in addition, 100nm aluminum film is arranged at the position except the maximum diameter of the dielectric super-oscillation ring band sheet for blocking the incident laser beam.
While the invention has been described in connection with specific embodiments thereof, it will be understood that these should not be construed as limiting the scope of the invention, which is defined in the following claims, and any variations which fall within the scope of the claims are intended to be embraced thereby.

Claims (8)

1. A design method of a dielectric super-oscillation ring band piece is characterized in that the method is based on the variable radial width and variable phase etching depth of a variable ring band of the dielectric super-oscillation ring band piece, and under the condition of laser beam vertical illumination, a diffraction light field in a vertical axis plane at any distance behind the dielectric super-oscillation ring band piece is calculated by using a vector angle spectrum theory and a fast Hankel conversion algorithm; setting the diameter, the ring belt number, the focal length, the minimum ring belt width and the maximum phase etching depth of the dielectric super-oscillation ring belt sheet; blocking incident laser beams by a metal-plated film in the area outside the diameter of the dielectric super-oscillation ring belt sheet; establishing an optimized objective function of a single focus or light needle focusing problem; optimizing and solving the etching width and the etching depth of the girdle by adopting a genetic algorithm to obtain a dielectric medium super-oscillation girdle plate structure meeting the design target; the method specifically comprises the following steps:
step one, giving the required diffraction light field intensity distribution characteristics of the dielectric super-oscillation annular zone plate, and respectively constraining the diffraction intensity field in the transverse direction and the axial direction according to the required diffraction light field intensity distribution to establish an optimized objective function and constraint conditions;
setting the diameter, the number of annuli, the maximum phase etching depth, the minimum annulus width and the focal length of the dielectric super-oscillation annuli, the wavelength and the polarization state of the illumination laser beam, and the dielectric material and the working medium of the dielectric super-oscillation annuli;
thirdly, under the parameter setting of the second step, calculating the light field intensity distribution in the vertical axis plane at any distance behind the super-oscillation ring band sheet through a vector angle spectrum theory and a fast Hankel transform algorithm;
step four, on the basis of the variable annular radial width and the variable phase etching depth of the dielectric super-oscillation annular plate, solving the dielectric super-oscillation annular plate structure meeting the optimization target established in the step one by adopting a genetic algorithm; the optimization design process of the genetic algorithm comprises the following steps:
401) and (3) carrying out an encoding operation: encoding the width and etching depth of each zone respectively, wherein the width of N zones passes through the interval [0, R ] between 0 and the radius R of the super-oscillation zone]N-1 dividing points generated internally at random are obtained, and the positions of the dividing points are coded by decimal numbers; phase etching depth phi of each ring belt of single ring belt sheetiThe same, coded by one decimal number, takes on the interval phii∈[0,π/2](ii) a The zone etching zone bit of the dielectric super-oscillation zone piece is coded by a one-bit binary number, the zone bit is 1 to indicate that the zone is etched, and the zone bit is 0 to indicate that the zone is not etched;
402) random generation of psThe initial individuals form an initial population, the loop widths of the initial individuals are checked, individuals which do not meet the requirement of the minimum loop width are removed, new individuals are regenerated until all the individuals in the initial population meet the requirement; then according to the stepsCalculating an optimized objective function value F of each individual by the optimized objective function established in the first stepi，i＝1,2,...,ps；
403) In order to improve the optimization design efficiency, constraint conditions in the optimization model are written into a set optimization objective function and are incorporated into a total objective function, and the ratio of the maximum light intensity in the dark field region required to be taken out of the dark field region to the central light intensity of the main lobe is taken as an objective function FdAnd are combined into a total objective function F with a set weighting coefficient to obtain F ═ w1/Fxy+w2/Fz+w3/Fd；
404) And (3) carrying out selective copying operation: the selection strategy adopts a method of combining an elite individual retention strategy and roulette, and directly copies the individual with the highest fitness in the contemporary population into the next generation without crossing and mutation operations; the other individuals are selected according to a roulette method by first determining respective selection probabilities according to respective fitness values of all individuals
Figure FDA0002475304300000021
Then in [0,1 ]]Randomly generating a random number r in the interval if
Figure FDA0002475304300000022
Then select individual i to copy to the next generation, where P0＝0；
405) Performing a cross operation: according to the cross probability PcRandomly generating a random number for every two individuals, if the random number is less than or equal to PcIf not, the two individuals are subjected to the cross operation; the crossing operation adopts a uniform crossing method, firstly, a binary crossing template with the same length as the parent individual is randomly generated, wherein 0 represents that the corresponding position is not exchanged, and 1 represents that the corresponding position is exchanged; after each pair of individuals are subjected to the cross operation, judging whether the generated new individuals meet the requirement of the minimum bandwidth, and if not, carrying out the cross operation again;
406) according to the mutation probability PmTo aim atEach individual randomly generates a random number if the random number is less than or equal to PmIf not, the individual does not carry out mutation operation; the variation operation adopts single point variation, if the variation point is a dividing point for determining the width of the ring band, then [0, R ] is taken]Random numbers uniformly distributed in the interval replace selected individual genes; if the variation is the annular phase etching depth of the dielectric super-oscillation annular plate, then [0, pi/2 ] is taken]Replacing the ring phase etching depth of the dielectric super-oscillation ring band piece by random numbers uniformly distributed in the interval; if the variation is the zone bit for determining whether each zone of the dielectric super-oscillation zone piece is etched, negating the zone bit, namely changing the zone etching 1 into the zone non-etching 0 or changing the zone non-etching 0 into the zone etching 1; judging whether the generated new individual meets the requirement of the minimum bandwidth after each individual mutation operation is finished, and if not, carrying out the mutation operation again;
407) generating a new offspring population after the selection, the crossing and the variation are finished, calculating objective function values of all individuals of the offspring population, replacing the original parent population with the new offspring population, returning to the step 404 of the genetic algorithm), carrying out a new iteration, and repeating the steps until the set iteration number N is reachedg；
408) Number of iterations completed NgThen, the genetic optimization process is finished, and the final optimization result is NthgThe individuals with the highest fitness in the generation group are required to be the dielectric super-oscillation annular belt structure which is close to or meets the set diffraction light field intensity distribution.
2. The method of claim 1, wherein the dielectric super-oscillating ring plate is a binary phase type super-oscillating ring plate, and the phase modulation of the incident light wave is realized by etching each ring zone on the surface of the dielectric material to a depth optimally set.
3. The method as claimed in claim 1, wherein the width of each ring zone included in the designed superoscillatory ring zone is variable, the phase etching depth of each ring zone of a single superoscillatory ring zone is uniform, the etching depth is variable for different superoscillatory ring zone, and the width of each ring zone and the etching depth are optimized and solved by genetic algorithm.
4. The method as claimed in claim 1, wherein in the step one, the diffraction light field intensity distribution characteristics of the dielectric super-oscillation ring strip include transverse full width half maximum, axial full width half maximum of the focusing light spot, or transverse full width half maximum, axial focal depth and axial light intensity uniformity of the focusing light needle.
5. The method for designing a dielectric super-oscillating ring strip according to claim 1 or 4, wherein in the first step, the specific method for establishing the optimized objective function is as follows: according to the required full width at half maximum and focal depth of the focusing light spot or the light needle, respectively finding out the half-height point of the transverse and axial focusing light spot or the light needle, and solving the ratio F of the light intensity at the position of the half-height point to the light intensity at the central position of the focusing light spot or the light needlexyAnd FzThe ratio is the established transverse and axial optimization objective function respectively; the optimization objective function in two directions passes through the set weighting coefficient w1And w2Are synthesized into a total optimization objective function F ═ w1/Fxy+w2/FzAnd converting the multi-objective optimization problem into a single-objective optimization problem.
6. The method according to claim 5, wherein the specific setting requirements of the superoscillatory ring band in step two are as follows: the diameter D is more than or equal to 5 lambda0，λ0The wavelength of the illumination laser in vacuum is in the range from X-ray to far infrared band, and the focal length satisfies that f is more than or equal to lambda0The number N of the ring belts is more than or equal to 2, and the maximum phase etching depth delta phimaxLess than or equal to pi/2 and the minimum annulus width delta rminMore than or equal to 200 nm; the polarization state of the illumination laser beam is linear polarization, circular polarization and radial polarizationOr angular polarization, refractive index n of dielectric materialdGreater than 1, the working medium is air, oil or water, the refractive index n of the working mediumw≥1。
7. The method for designing the dielectric super-oscillation ring band piece according to claim 1, wherein the vector angular spectrum theory in the third step is that firstly, an angular spectrum of an emergent light field on the rear surface of the microstructure is obtained through Fourier transform, and then, each polarization component of a plane light field at an observation position is obtained through inverse Fourier transform, so that the intensity distribution of the light field in any distance vertical axis plane after the super-oscillation ring band piece is vertically illuminated by the laser beam is obtained through calculation; the fast Hankel transformation algorithm is a fast and high-precision calculation method for calculating cross-correlation by utilizing Fourier transformation by performing variable replacement by utilizing a nonlinear exponential function in a standard Hankel transformation integral expression and expressing standard unilateral Hankel transformation as bilateral cross-correlation integral.
8. The method as claimed in claim 6, wherein the phase etching depth of the designed dielectric super-oscillating ring strip is corresponding to the real etching depth of the dielectric
Figure FDA0002475304300000041
φiFor phase etch depth, ndAnd nwDielectric and working medium refractive indices, respectively; phase etching depth phi of dielectric super-oscillation ring band plateiThe zone of (a) corresponds to a phase modulation function of ti(r)＝exp(-jφi),ri-1≤r＜ri。
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